We have enjoyed the series of articles in Journal of Medical Toxicology’s new section “Biostatistics and Epidemiology for the Toxicologist.” A recent article provided excellent guidance on using statistical measures of central tendency — the mean, median, and mode — to describe a population [1]. We would like to highlight the particular and pragmatic challenge of characterizing the epidemiology of pediatric poisoning.
Poisoning events from birth through adolescence have many root causes, but the two predominant phenomena reported to poison centers are as follows: (a) exploratory ingestions by ambulatory preschool-aged children and (b) intentional ingestions by adolescents. This may lead to a bimodal pattern with two Gaussian distributions within a single dataset of subjects. Figure 1 represents a hypothetical, fictitious age histogram for pediatric edible THC exposures that was created for the purpose of illustration. This distribution is typical for pediatric poisoning with few poisonings among pre-mobile children, a rise in exploratory cases among toddlers, a decline in cases in among early school-aged children, and another rise in cases among adolescents with intent.
Fig. 1.
A hypothetical dataset of “pediatric” patients presenting for poisoning from edible THC products. Note: This dataset demonstrates a bimodal distribution (typical for pediatric poisoning research datasets) with one distinct population with a mean age of 3 years and another population with mean age of 15 years
Mohan and Su advise, “When determining which measure of central tendency to report in a scientific manuscript, it is essential to consider how the data are distributed.” Take note that if a researcher tried to describe the results in Fig. 1 by lumping it all into a single mean or median, reporting the mean age of 9.5 years or the median age of 12 years would be a poor description of this data. The “average patient” in this group is not best characterized as being 10 years old. Researchers are encouraged to think about potential differences in exposure pathways, or in physiology, among study subjects, and to appropriately consider those differences in both study design and in statistical presentation. Creation of an age histogram can be very informative, and as demonstrated in Table 1, it is possible to define different populations more clearly within a single dataset.
Table 1.
Illustration of different mean values derived from dataset (Fig. 1) based upon selection of age cutoffs
| Age group (years) | Mean age [mathematical, rounded] | Mean age [significanta] |
|---|---|---|
| 1–18 | 9.5 | 10 |
| 1–6 | 3.3 | 3 |
| 7–12 | 10.8 | 11 |
| 13–18 | 15.1 | 15 |
| 1–9 | 3.5 | 4 |
| 10–18 | 14.9 | 15 |
The precision of point estimates, such as mean, is influenced by sample size. It is possible to provide 95% confidence intervals for these point estimates
aMathematically, calculations of mean will result in a variable number of decimal places. In instances, such as here, where discreet datapoints were measured and recorded in whole integers, reporting of scientifically valid significant digits may be more appropriate
Footnotes
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Reference
- 1.Mohan S, Su MK. Biostatistics and epidemiology for the toxicologist: measures of central tendency and variability – where is the “middle?” and what is the “spread?”. J Med Toxicol. 2022;18:235–238. doi: 10.1007/s13181-022-00901-7. [DOI] [PMC free article] [PubMed] [Google Scholar]